TransferFunctionCancel

TransferFunctionCancel[tfm]

cancels common poles and zeros in the TransferFunctionModel tfm.

TransferFunctionCancel[tfm,crit]

cancels only common pole-zero pairs ei for which crit[ei] is True.

Details and Options

Examples

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Basic Examples  (3)

Cancel common pole-zero pairs:

Cancel common pole-zero pairs that are stable:

Cancel stable pairs within a specified tolerance:

Scope  (7)

Cancel the common pole-zero pair at the origin:

Cancel common pole-zero pairs of a fourth-order system:

The common pole-zero pair is evident by factoring the transfer function:

Cancel pole-zero pairs for a discrete-time system:

Cancel pole-zero pairs for a system with input delay:

Cancel common pole-zero pairs that are stable:

Cancel pole-zero pairs with tolerance not greater than 0.01:

With zero tolerance nothing is canceled:

This system has two pole-zero pairs whose tolerance is less than or equal to 0.6:

Cancel the pair with frequency greater than 9 radians per time unit:

Visualize the responses of the three systems to a unit step input:

Options  (2)

Tolerance  (2)

The tolerance is zero by default:

Cancel pole-zero pairs whose absolute difference is not greater than 0.15:

Pole-zero cancellation with a larger tolerance:

Applications  (1)

Use TransferFunctionCancel to obtain a simpler representation of a highly oscillatory system in a series with a notch filter:

A system of higher order is obtained without the cancellation:

In most cases the pole-zero cancellation has a negligible effect on the overall dynamics:

Properties & Relations  (1)

TransferFunctionCancel is equivalent to MinimalStateSpaceModel for SISO systems:

Possible Issues  (2)

A system with an unstable pole-zero cancellation may appear stable:

But it is internally unstable:

TransferFunctionCancel does not support internal delays:

Wolfram Research (2010), TransferFunctionCancel, Wolfram Language function, https://reference.wolfram.com/language/ref/TransferFunctionCancel.html.

Text

Wolfram Research (2010), TransferFunctionCancel, Wolfram Language function, https://reference.wolfram.com/language/ref/TransferFunctionCancel.html.

BibTeX

@misc{reference.wolfram_2021_transferfunctioncancel, author="Wolfram Research", title="{TransferFunctionCancel}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/TransferFunctionCancel.html}", note=[Accessed: 28-July-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_transferfunctioncancel, organization={Wolfram Research}, title={TransferFunctionCancel}, year={2010}, url={https://reference.wolfram.com/language/ref/TransferFunctionCancel.html}, note=[Accessed: 28-July-2021 ]}

CMS

Wolfram Language. 2010. "TransferFunctionCancel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TransferFunctionCancel.html.

APA

Wolfram Language. (2010). TransferFunctionCancel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TransferFunctionCancel.html